Time series copulas for heteroskedastic data

Abstract

Summary We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We suggest copulas for first‐order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co‐movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value‐at‐risk forecasts.

Modelling Volatile Time Series with V-Transforms and Copulas

“…These models are based on the pair-copula apporoach developed in Joe (1996), Cooke (2001, 2002) and Aas et al (2009). However, the standard bivariate copulas that enter these models are not generally effective at describing the typical serial dependencies created by stochastic volatility, as observed by Loaiza-Maya et al (2018). The paper is structured as follows.…”

Exploring a copula-based alternative to additive error models—for non-negative and autocorrelated time series in hydrology

“…where F t () is the cumulative probability distribution of the corresponding density f t () (Loaiza-Maya et al, 2018). The copula can be simplified if a Markov property is assumed for the time series.…”

Parametric Conditional Mean Inference With Functional Data Applied to Lifetime Income Curves

“…studies applying mixture copula models (e.g., Dias and Embrechts, 2004;Chen and Fan, 2006;Hu, 2006;Lai et al, 2009;Diks et al, 2010;Zimmer, 2012;Kosmidis and Karlis, 2016;Loaiza-Maya et al, 2018). But methods of inference concerning homogeneity in dependence structures based on finite mixture copula models has, to the best of our knowledge, so far not been addressed.…”